Itzjbean is correct, without a proper nestbox with bedding in the bottom of it, you will end-up with a bunch of splayed-leg chicks. So you need to go to the pet shop and buy a wooden nest box that is large enough for an Eclectus and babies to be inside, and then buy some bedding, such as Care-Fresh, the paper bedding, and put a layer in the bottom...They will toss the bedding outside of nestbox, that's normal, just add more. If the babies are standing/walking on a bare floor they will develop splay-legs, the bedding keeps their legs together while they grow and develop.
I'm assuming this is an Eclectus, so the incubation period for the eggs is around 28 days I believe, but remember that all the eggs are different ages (usually laid a day or two apart), so it's 28 days from the time each, individual egg is laid.
It's normal for the mother to pluck her feathers out to both line the nest and to make her belly/chest bare to place against the eggs...it's not from stress at all, it's normal.
Please do a lot more research, as you may very well have to take-over hand-feeding the babies if mom dies, if mom/dad kick the babies out of the nestbox, if they refuse to feed them, if they start plucking them/hurting them, etc. You need to have all necessary, non-optional equipment on-hand BEFORE any eggs hatch. And then you'll need to check on the babies crops to make sure that they are being fed, and check them multiple times a day. You need:
-Commercial baby bird hand-feeding formula (Kaytee, Roudybush are the two most common)
-Candy/Cooking Thermometer with a metal probe to keep in the formula while feeding the babies (formula must ALWAYS be between 104 degrees F and 110 degrees F, not one degree cooler, not one degree hotter)
-Oral Syringe
-Potentially be ready to make a homemade Brooder if the babies are kicked out of the nestbox, as they must be kept at 95 degrees F at all times before they grow-in all their down feathers, and then between 80-85 degrees F at all times once they grow-in their down but before their outer feathers fully grow-in (if they are not kept at these temps they can die from exposure, as they cannot regulate their own body temps before getting their down/feathers, and also just the same as what can happen if the formula is too cold, if their ambient temperature is too cold they will quickly develop a GI/Crop Yeast/Fungal infection, Crop-Stasis, and death...So to make a homemade Brooder you need an ambient temperature you can place in the back of a cardboard box or glass aquarium, an electric heating-pad that you can adjust the heat on, and the same bedding
***This is not optional stuff, and you must be able to take-over hand-feeding the babies at a moment's notice or they will die. During the first 2-3 weeks they have to be fed every 2-3 hours, including overnight. Only at 4 weeks old can they go 6-8 hours overnight without eating. So it's a big deal and a pain in the butt. Set your alarm and wake-up every 2-3 hours. It's rough. But you always have to be ready to take-over or the chicks will die...Also, please read-up on "Proper baby bird hand-feeding technique", as it is extremely easy to Aspirate formula into their lungs if you don't know how to hand-feed them with an oral syringe, and it can kill them instantly, or at the very least cause Aspiration Pneumonia. There is a proper technique, a correct side of the beak to go in at, a correct side to angle towards, you have to learn about their feeding-response, etc. So please prepare yourself...